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11 total. Dimension 4 – Docking Station was the debut concert tour of South Korean girl group f (x) launched in support of their fourth studio album, 4 Walls. It consisted of three shows in Seoul, South Korea, and eight shows throughout Japan. The tour commenced at the Olympic Hall in Seoul, and concluded at the Yokohama Arena in Yokohama, Japan.
Mathematically, a four-dimensional space is a space that needs four parameters to specify a point in it. For example, a general point might have position vector a, equal to. This can be written in terms of the four standard basis vectors (e1, e2, e3, e4), given by. so the general vector a is.
An associate of the School of Paris —a group of avant-gardists including Pablo Picasso, Guillaume Apollinaire, Max Jacob, Jean Metzinger, and Marcel Duchamp —Princet is credited with introducing the work of Henri Poincaré and the concept of the "fourth dimension" to the cubists at the Bateau-Lavoir during the first decade of the 20th century.
The Fourth Dimension: Toward a Geometry of Higher Reality (1984) is a popular mathematics book by Rudy Rucker, a Silicon Valley professor of mathematics and computer science. It provides a popular presentation of set theory and four dimensional geometry as well as some mystical implications. A foreword is provided by Martin Gardner and the 200 ...
The regular complex polytope 4 {4} 2, , in has a real representation as a tesseract or 4-4 duoprism in 4-dimensional space. 4 {4} 2 has 16 vertices, and 8 4-edges. Its symmetry is 4 [4] 2, order 32. It also has a lower symmetry construction, , or 4 {}× 4 {}, with symmetry 4 [2] 4, order 16. This is the symmetry if the red and blue 4-edges are ...
Dimension 4 is an anthology of science fiction short stories edited by Groff Conklin. It was first published in paperback by Pyramid Books in February 1964. [1] The book collects four novelettes by various science fiction authors. The stories were previously published from 1942-1958 in the science fiction magazines Astounding Science Fiction ...
4-manifold. In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. There exist some topological 4-manifolds which admit no smooth structure, and even if ...
It is a highly non-trivial generalization of the classic Gauss–Bonnet theorem (for 2-dimensional manifolds / surfaces) to higher even-dimensional Riemannian manifolds. In 1943, Carl B. Allendoerfer and André Weil proved a special case for extrinsic manifolds. In a classic paper published in 1944, Shiing-Shen Chern proved the theorem in full ...